BCH codes form a class of parameterized, error-correcting codes that were developed by Alexis Hocquenghem, and independently by Raj Chandra Bose and Dwijendra Kumar Ray-Chaudhuri. The acronym “BCH” is formed simply from initials of the three individuals named above. A principal advantage of BCH codes is that decoding can be performed via an elegant algebraic method known as syndrome decoding.
Syndrome decoding is of relatively low complexity, and can be performed by very simple, low-level electronic hardware. BCH codes are thus very popular for low power communication systems, and decoding devices utilizing BCH codes can be made very small. BCH code is employed in communication systems such as deep space communication, digital subscriber loops (DSL), and short range wireless communication systems. Additional applications of BCH codes include biomedical devices communicating measurements of physical data measured inside the body. Examples of communication standards for such biomedical devices include IEEE standard P802.15.6 (Personal Area Network Physical Layer Standard) and IEEE standard P802.15-09-0329-00-0006 (Wireless Personal Area Networks Standard, also referred to as the MedWiN Physical Layer Proposal).
In general, BCH decoding includes three modules: a syndrome computation module, an Error Locator Polynomial (ELP) solver module, and a Chien search and error evaluator module. Conventional ELP solver modules employ an iterative algorithm to determine the coefficients of an error locator polynomial, thereby providing the location of error bits in encoded BCH code. Embodiments disclosed herein presents a closed-form solution to a scaled error locator polynomial that reduces complexity in the ELP solver module as well as in a decoder device overall.